where \(\Phi (\cdot )\)  represents the kernel feature mapping and \(\lambda \)  is the
regularization parameter. Due to the Fenchel duality theorem [1]},
the dual formulation of this problem is:
\(\min _{\alpha \in ^n} \frac{1}{2n} \alpha ^\top \alpha + \frac{\lambda }{2}\sum _{i=1}^{n}\left(\alpha _i^2 + 2\alpha _i y_i\right),\) 
